Hi Maria,
I did the Trans-Siberian trip in 2008 and it was well worth it. Of course there are many ways to do it: independently, with friends, with a tour group, etc. I went with a tour group (Intrepid Travel). The reason I went with a tour group is because I wanted the safety, planning, and organization of a professional (especially through these parts of the world) and the reason I used Intrepid Travel is because they use only small groups (12 people max), local transport (no big tour buses), and are sensitive to local economy, culture, etc.
There are a number of different routes. The route I took started in Beijing, China, went through Mongolia, and ended in St. Petersburg, Russia. The whole trip took three weeks though it really only takes maybe seven days of straight train travel to get from one end to the other. This is if you literally do not get off the train. I found the train to be very comfortable. The typical train cabin consists of four beds and the two lower beds convert into seating during the day when people aren't sleeping. My tour used these cabins. However, I believe there might be luxury level tours that use the private 2-bed rooms, which come with a sink and possibly a toilet. For everyone else, there are shared toilets at either end of each train car. There are no showers anywhere on the train. If traveling independently I suppose you can choose when and where you want to disembark and stay a few nights in a town along the way, but because I was on a tour, I was committed to the tour schedule. The longest train segment was four days and three nights with random stops that averaged about 15 minutes to half and hour. At these stops you can go into the train station and buy food or take a walk.
I could go on at length about this trip and share my photos with you if you're interested. But back to answering your question, I found the train journey comfortable. It matters who you're sharing the cabin with. I was with fellow tour group members, but there were two other tour group members that had to share with strangers and their experience was not so good. I took the trip not as a means of transport from China to Russia, because if that's all you're looking to do, then it's obviously far more practical and economical to take a plane, but rather, I wanted to experience the journey of crossing countries, continents, cultures, and time zones (the last is a very interesting experience, you're constantly changing the time on your watch because of how many time zones are traversed). In addition to the landscape, it's amazing to gradually see how peoples' faces change, even within a country and ethnicity, as you slowly make your way from east to west.